Confocal surface topography measurement with fixed focal positions

ABSTRACT

An apparatus is described for measuring surface topography of a three-dimensional structure. In many embodiments, the apparatus is configured to focus each of a plurality of light beams to a respective fixed focal position relative to the apparatus. The apparatus measures a characteristic of each of a plurality of returned light beams that are generated by illuminating the three-dimensional structure with the light beams. The characteristic is measured for a plurality of different positions and/or orientations between the apparatus and the three-dimensional structure. Surface topography of the three-dimensional structure is determined based at least in part on the measured characteristic of the returned light beams for the plurality of different positions and/or orientations between the apparatus and the three-dimensional structure.

CROSS-REFERENCE

This application is a continuation application of Ser. No. 14/323,237,filed Jul. 3, 2014, which is incorporated herein by reference in itsentirety.

BACKGROUND

A variety of approaches have been developed for measuring surfacetopography optically. For example, optical systems and methods have beendeveloped and employed that can be used to optically measure surfacetopography of a patient's teeth. The measured surface topography of theteeth can be used, for example, to design and manufacture a dentalprosthesis and/or to determine an orthodontic treatment plan to correcta malocclusion.

One technique for measuring surface topography optically employs lasertriangulation to measure distance between a surface of the tooth and anoptical distance probe, which is inserted into the oral cavity of thepatient. Surface topography measured via laser triangulation, however,may be less accurate than desired due to, for example, sub-optimalreflectivity from the surface of the tooth.

Other techniques for measuring surface topography optically, which areembodied in CEREC-1 and CEREC-2 systems commercially available fromSiemens GmbH or Sirona Dental Systems, utilize the light-section methodand phase-shift method, respectively. Both systems employ a speciallydesigned hand-held probe to measure the three-dimensional coordinates ofa prepared tooth. Both of these approaches, however, require a specificcoating (i.e. measurement powder and white-pigments suspension,respectively) to be deposited on the tooth. The thickness of the coatinglayer should meet specific, difficult to control requirements, which canlead to inaccuracies in the measurement data.

In yet another technique, mapping of teeth surface topography is basedon physical scanning of the surface by a probe and by determining theprobe's position, e.g., by optical or other remote sensing means.

U.S. Pat. No. 5,372,502 discloses an optical probe for three-dimensionalsurveying. Various patterns are projected onto the tooth or teeth to bemeasured and a corresponding plurality of distorted patterns arecaptured by the optical probe. Each captured pattern can be used torefine the topography measurement.

SUMMARY

Apparatus and methods for measuring surface topography of athree-dimensional structure are provided. In many embodiments, anapparatus for measuring surface topography is configured to illuminatethe three-dimensional structure (e.g., a patient's dentition) with lightbeams for a plurality of different positions and/or orientations betweenan optical probe of the apparatus and the three-dimensional structure.The apparatus and methods disclosed employ confocal scanning of thethree-dimensional structure without optically moving the focal positionsof the light beams relative to the optical probe, but instead usemovement of the optical probe relative to the structure, thus enablingsmaller, faster, and more cost-effective optics.

Thus, in one aspect, an apparatus is described for measuring surfacetopography of a three-dimensional structure. The apparatus is configuredto measure a characteristic of each of a plurality of returned lightbeams that are generated by illuminating the three-dimensional structurewith a plurality of light beams. The characteristic is measured for aplurality of different positions and/or orientations between theapparatus and the three-dimensional structure.

In another aspect, an apparatus is described for measuring surfacetopography of a three-dimensional structure. In many embodiments, theapparatus includes an optical probe, an optical system, and a processingunit. The optical probe is moved relative to the three-dimensionalstructure. The optical system focuses each of a plurality of incidentlight beams to a respective focal position relative to and distal to theoptical probe. Returned light beams are generated by illuminating thethree-dimensional structure with the incident light beams. Theprocessing unit determines surface topography of the three-dimensionalstructure based at least in part on a measured characteristic of thereturned light beams for a plurality of different relative positionsand/or orientations between the optical probe and the three-dimensionalstructure.

In another aspect, a method is described for measuring surface topologyof a three-dimensional structure. The method includes focusing each of aplurality of incident light beams to a respective focal point relativeto and distal to an optical probe. Returned light beams are generated byilluminating the three-dimensional structure with the incident lightbeams. A characteristic of the returned light beams is measured for aplurality of different relative positions and/or orientations betweenthe optical probe and the three-dimensional structure to generatesurface topography data for the three-dimensional structure.

Other objects and features of the present invention will become apparentby a review of the specification, claims, and appended figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings of which:

FIGS. 1A and 1B schematically illustrate, by way of a block diagram, aconfocal surface topography measurement apparatus in accordance withmany embodiments (FIG. 1B is a continuation of FIG. 1A);

FIG. 2A is a top view of a probing member of a confocal surfacetopography measurement apparatus, in accordance with an embodiment;

FIG. 2B is a longitudinal cross-section through the probing member ofFIG. 2A, depicting exemplary rays passing therethrough;

FIGS. 2C and 2D are end views of the probing member of FIG. 2A, inaccordance with many embodiments;

FIG. 3A illustrates an optical probe scanning a structure using fixedfocal positions, in accordance with many embodiments;

FIG. 3B shows another view of the optical probe of FIG. 3A duringscanning of the structure using fixed focal positions;

FIG. 4A illustrates an optical assembly configured to focus a pluralityof light beams to respective focal positions, in accordance with manyembodiments;

FIG. 4B illustrates another optical assembly configured to focus aplurality of light beams to a diagonal focal plane, in accordance withmany embodiments;

FIG. 5 illustrates a micro lens array for focusing an array of lightbeams to a diagonal focal plane, in accordance with many embodiments;

FIG. 6A illustrates another optical assembly configured to focus aplurality of light beams to a diagonal focal plane, in accordance withmany embodiments;

FIG. 6B illustrates the optical path of returning light beams throughthe optical assembly of FIG. 6A, in accordance with many embodiments;

FIG. 7A illustrates another optical assembly configured to focus aplurality of light beams to a diagonal focal plane, in accordance withmany embodiments;

FIG. 7B illustrates an unfolded configuration of the optical assembly ofFIG. 7A; and

FIG. 8 is a simplified block diagram depicting acts of a method formeasuring surface topography using fixed focal positions, in accordancewith many embodiments.

DETAILED DESCRIPTION

Apparatus and methods are described herein that employ confocalmeasurement of surface topography. In some approaches, such as thosedescribed in U.S. Pat. No. 6,697,164, the disclosure of which is hereinincorporated by reference in its entirety, incident light beamsgenerated by a measurement apparatus are used to determine the surfacetopography of a three-dimensional structure. The apparatus includes anoptical probe from which the light beams emanate in order to illuminatethe structure. The light beams are focused by focusing optics torespective focal points (also known as focal positions) external to theoptical probe. The focal positions are optically scanned through aplurality of positions relative to the optical probe in order to measurethe three-dimensional surface topography. The focal positions are movedrelative to the optical probe along a direction of propagation of theincident light beams (axial scanning). The focal positions can also bemoved orthogonal to the direction of propagation (transverse scanning).Any description herein relating to a direction of light can be regardedas referring to a direction of the principal rays (chief rays) of thelight. Similarly, any description herein relating to a direction ofpropagation of light can be regarded as referring to a direction ofpropagation of the principal rays of the light. Typically, axial and/ortransverse scanning relative to the optical probe is achieved bymechanically moving an optical element, for example via suitabledevices, such as galvanometric mirrors, motors, and/or telescopicscanning mechanisms. The use of such axial or transverse scanningcomponents, however, may increase the size, weight, and cost of themeasurement apparatus.

In contrast, the apparatus and methods of the present disclosure performconfocal measurement of three-dimensional surface topography withoutoptically moving the position of the focal positions relative to theoptical probe. In contrast to the above-described approaches thatoptically scan the focal positions relative to the optical probe, theapproaches described herein focus each light beam to a respective focalpoint having a fixed spatial disposition relative to the optical probe.Relative movement between the optical probe and the three-dimensionalstructure is used to move the focal points relative to the structure.Distances between the optical probe and the three-dimensional structureare measured for a plurality of different positions and/or orientationsbetween the optical probe and the three-dimensional structure. The datais then processed in conjunction with data regarding the relativeposition between the probe and the three-dimensional structure todetermine surface topography of the measured structure. By avoiding theuse of optical scanning mechanisms, the apparatus and methods disclosedherein may be smaller, faster, and more cost-effective relative toexisting optical measurement systems.

In many embodiments, the distance between the optical probe and thethree-dimensional structure is determined by measuring one or morecharacteristics of returning light beams generated by illuminating thestructure with the incident light beams. Such characteristics caninclude, for example, intensity, wavelength, polarization, phase shift,interference, and/or dispersion of the returning light beams. Anydescription herein relating to light intensity can also be applied toother suitable characteristics of light, and vice-versa. Themeasurements of the characteristic(s) can be used to detect whether theincident light beams are focused on the surface of the structure andthereby determine the distance between the optical probe and thethree-dimensional structure.

For example, the surface topography of the structure can be determinedbased on measuring the intensities of the returning light beams. In manyembodiments, the apparatus is configured such that the intensity of anyparticular light beam returning from the structure is maximized when theincident light beam is focused on the surface of the structure. Bymoving the probe relative to the structure, a distance between the probeand the structure for a particular light beam and position andorientation of the probe relative to the structure can be determined byidentifying when the intensity of the respective returning reflectedlight beam is maximized. The surface topography of the structure canthen be determined based on the measured intensities of the returnedlight beams and the position and/or orientation of the optical proberelative to the structure.

As another example, the surface topography can be determined by usingspatial frequency analysis to identify which regions of the structureare in focus. In many embodiments, focused regions will contain higherspatial frequencies than out of focus regions. Accordingly, a distancebetween the probe and a specified region on the structure for aparticular position and orientation of the probe relative to thestructure can be determined by identifying when the spatial frequenciesof the region are maximized. This approach can be applied to determinethe surface topography of structures having spatial details.

The apparatus and methods described herein can be used to measure thesurface topography of any suitable three-dimensional structure. In manyembodiments, optical measurements are taken to generate datarepresenting the three-dimensional surface topography of a patient'sdentition. The data can be used, for example, to produce athree-dimensional virtual model of the dentition that can be displayedand manipulated. The three-dimensional virtual models can be used to,for example, define spatial relationships of a patient's dentition thatare used to create a dental prosthesis (e.g., a crown or a bridge) forthe patient, provide a digital model or a physical model for recordkeeping purposes, set up a treatment plan, fabricate orthodonticappliances, or any other dental purpose. The surface topography data canbe stored and/or transmitted or output, such as to a manufacturingdevice that can be used to, for example, make a physical model of thepatient's dentition that is used by a dental technician to create adental prosthesis for the patient.

In one aspect, an apparatus is provided for measuring surface topographyof a three-dimensional structure. The apparatus can be configured to:(a) focus each of a plurality of light beams to a respective fixed focalposition relative to the apparatus; (b) measure a characteristic of eachof a plurality of returned light beams that are generated byilluminating the three-dimensional structure with the light beams, thecharacteristic being measured for a plurality of different positionsand/or orientations between the apparatus and the three-dimensionalstructure; and (c) determine surface topography of the three-dimensionalstructure based at least in part on the measured characteristic of thereturned light beams for the plurality of the different positions and/ororientations between the apparatus and the three-dimensional structure.

In another aspect, an apparatus is provided for measuring surfacetopography of a three-dimensional structure. The apparatus includes anoptical probe configured to be moved relative to the three-dimensionalstructure. The apparatus includes an illumination unit configured togenerate a plurality of incident light beams, each of the incident lightbeams comprising a first wavelength component. The apparatus includes anoptical system configured to focus the first wavelength component ofeach of the plurality of incident light beams to a respective fixedfocal position relative to the optical probe. The apparatus includes adetector unit configured to measure a characteristic of each of aplurality of returned light beams that are generated by illuminating thethree-dimensional structure with the incident light beams. The apparatusincludes a processing unit coupled with the detector unit and configuredto determine surface topography of the three-dimensional structure basedat least in part on the measured characteristic of the plurality ofreturned light beams for a plurality of different relative positionsand/or orientations between the optical probe and the three-dimensionalstructure. In many embodiments, the characteristic is intensity.

In many embodiments, the detector unit includes a two-dimensional arrayof sensor elements. Each sensor element can be configured to measure thecharacteristic for a corresponding returned light beam of the pluralityof returned light beams. The optical system can be configured to form atwo-dimensional pattern of the incident light beams from light generatedby the illumination unit, the two-dimensional pattern of incident lightbeams corresponding to the returned light beams measured by thetwo-dimensional array of sensor elements. The optical system can includean optics expander unit configured to expand light generated by theillumination unit to form the two-dimensional pattern of the incidentlight beams. The illumination unit can be configured to produce atwo-dimensional pattern of the incident light beams corresponding to thereturned light beams measured by the two-dimensional array of sensorelements.

The incident light beams can be focused to a plurality of respectivefocal lengths relative to the optical probe. In many embodiments, theincident light beams can be arranged in a plurality of rows having afirst row and a last row. The incident light beams in each row can befocused to a respective common focal length. The focal lengths of thefirst row and the last row can be different by a predetermined length.For example, the predetermined length can be from 5 mm to 25 mm. Thesensor elements can be arranged in a plane that is oriented for confocalsensing of the returned light beams relative to focal lengths of thefirst wavelength component of the incident light beams. In someembodiments, the plane of the sensor elements is non-orthogonal to thereturned light beams.

In many embodiments, the optical probe is moved through a plurality ofdifferent positions and/or orientations relative to the structure. Thethree-dimensional surface topography can thus be reconstructed from themeasured characteristic based at least in part on the position and/ororientation of the optical probe relative to the three-dimensionalstructure. Any suitable method can be used to determine the relativeposition and/or orientation between the optical probe and the structure.In many embodiments, the processing unit includes one or more processorsand a tangible non-transitory storage device. The tangiblenon-transitory storage device can store instructions executable by theone or more processors to cause the one or more processors to processdata of the measured characteristic generated using the detector unitfor the plurality of different relative positions and/or orientationsbetween the optical probe and the three-dimensional structure. The datacan be processed by the one or more processors to determine relativeposition and/or orientation between the optical probe and thethree-dimensional structure.

In many embodiments, the apparatus further includes a motion trackingdevice configured to collect motion data. The processing unit caninclude one or more processors and a tangible non-transitory storagedevice. The tangible non-transitory storage device can storeinstructions executable by the one or more processors to cause the oneor more processors to process the motion data to determine relativeposition and/or orientation between the optical probe and thethree-dimensional structure. For example, the motion tracking device caninclude a camera and the motion data can include image data. In anotherexample, the motion tracking device can include a gyroscope and/or anaccelerometer. As a further example, the motion tracking device caninclude an electromagnetic sensor.

Any suitable configuration of the plurality of incident light beams canbe used. For example, the optical system can be configured to focus thefirst wavelength component of the light beams to at least 10 differentfocal lengths relative to the scanner, and the focal lengths can have arange of at least 10 mm.

In another aspect, a method is provided for measuring surface topographyof a three-dimensional structure. The method can include generating aplurality of incident light beams, each of the incident light beamsincluding a first wavelength component. The first wavelength componentof each of the incident light beams can be focused to a respective focalposition relative to an optical probe. A characteristic of each of aplurality of returned light beams that are generated by illuminating thethree-dimensional structure with the incident light beams can bemeasured for a plurality of different relative positions and/ororientations between the optical probe and the three-dimensionalstructure. The measured characteristic for the plurality of differentrelative positions and/or orientations between the optical probe and thethree-dimensional structure can be processed to generate surfacetopography data for the three-dimensional structure. The surfacetopography for the three-dimensional structure can be generated usingthe surface topography data. In many embodiments, the measuredcharacteristic is intensity. In many embodiments, the method includestracking changes in relative position and/or orientation between theoptical probe and the three-dimensional structure.

The incident light beams can be arranged in a plurality of rows having afirst row and a last row. For example, the incident light beams in eachrow can be focused to a respective common focal length. The focallengths of the first row and the last row can be different by apredetermined length. For example, the predetermined length can be atleast 10 mm. The incident light beams can be focused to any suitablerespective fixed positions relative to the probe. For example, thewavelength component of the light beams can be focused to at least 10different focal lengths relative to the scanner, and the focal lengthscan have a range of at least 10 mm.

Turning now to the drawings, in which like numbers designate likeelements in the various figures, FIGS. 1A and 1B illustrate an apparatus20 for measuring surface topography optically. The apparatus 20 includesan optical device 22 coupled to a processor 24. The illustratedembodiment is particularly useful for measuring surface topography of apatient's teeth 26. For example, the apparatus 20 can be used to measuresurface topography of a portion of the patient's teeth where at leastone tooth or portion of tooth is missing to generate surface topographydata for subsequent use in design and/or manufacture of prosthesis forthe patient (e.g., a crown or a bridge). It should be noted, however,that the invention is not limited to measuring surface topography ofteeth, and applies, mutatis mutandis, also to a variety of otherapplications of imaging of three-dimensional structure of objects (e.g.,for the recordal of archaeological objects, for imaging of athree-dimensional structure of any suitable item such as a biologicaltissue, etc.).

The optical device 22 includes, in the illustrated embodiment, a lightsource (e.g., semiconductor laser unit 28) emitting a light, asrepresented by arrow 30. The light beam 30 can include a singlewavelength component or multiple wavelength components. In someinstances, light with multiple wavelength components can be generated bya plurality of light sources. The light passes through a polarizer 32,which causes the light passing through the polarizer 32 to have acertain polarization. The light then enters into an optic expander 34,which increases the diameter of the light beam 30. The light beam 30then passes through a module 38, which can, for example, be a grating ora micro lens array that splits the parent beam 30 into a plurality oflight beams 36, represented here, for ease of illustration, by a singleline.

The optical device 22 further includes a partially transparent mirror 40having a small central aperture. The mirror 40 allows transfer of lightfrom the laser unit 28 through the downstream optics, but reflects lighttravelling in the opposite direction. It should be noted that inprinciple, rather than a partially transparent mirror, other opticalcomponents with a similar function may be used (e.g., a beam splitter).The aperture in the mirror 40 improves the measurement accuracy of theapparatus. As a result of this mirror structure, the light beams producea light annulus on the illuminated area of the imaged object as long asthe area is not in focus. The annulus becomes a sharply-focusedilluminated spot when the light beam is in focus relative to the imagedobject. Accordingly, a difference between the measured intensity whenout-of-focus and in-focus is larger. Another advantage of a mirror ofthis kind, as opposed to a beam splitter, is that internal reflectionsthat occur in a beam splitter are avoided, and hence the signal-to-noiseratio is greater.

The optical device 22 further includes focusing optics 42, relay optics44 and an endoscopic probe member 46. The focusing optics 42 can includesuitable optics for focusing the light beams 36 to a plurality ofrespective focal points at fixed spatial dispositions relative to theprobe member 46, as described below. In many embodiments, the focusingoptics 42 is static, such that the optical device 22 does not employmechanisms to scan the focal points (e.g., axially or transversely)relative to the probe member 46. In many embodiments, the relay optics44 is configured to maintain a certain numerical aperture of the lightbeam's propagation.

The endoscopic probe member 46 can include a light-transmitting medium,which can be a hollow object defining within it a light transmissionpath or an object made of a light-transmitting material (e.g., a glassbody or tube). The light-transmitting medium may be rigid or flexible(e.g., fiber optics). In many embodiments, the endoscopic probe member46 includes a mirror of the kind ensuring total internal reflection anddirecting the incident light beams towards the patient's teeth 26. Theendoscope 46 thus emits a plurality of incident light beams 48 impingingon to the surface of the patient's teeth 26.

The endoscope 46 can include one or more motion tracking elements 47(e.g., a gyroscope, an accelerometer, targets for optical tracking, anelectromagnetic sensor). In many embodiments, the motion trackingelement 47 generates a motion tracking signal in response to movement ofthe endoscope 46. In many embodiments, the motion tracking signal isprocessed by the processor 24 to track changes in spatial disposition ofthe endoscope 46 in six degrees of freedom (i.e., three translationaldegrees of freedom and three rotational degrees of freedom).

In many embodiments, the incident light beams 48 form a two-dimensionalarray of light beams arranged in a plane, relative to a Cartesianreference frame 50, and propagating along the Z-axis. The light beams 48can be focused to respective focal points defining a suitable focalplane, such as a plane orthogonal to the Z axis (e.g., an X-Y plane) ora non-orthogonal plane. When the incident light beams 48 are incidentupon an uneven surface, the resulting array of illuminated spots 52 aredisplaced from one another along the Z-axis, at different (X_(i), Y_(i))locations. Thus, while an illuminated spot 52 at one location may be infocus for a given relative spatial disposition between the endoscope 46and the teeth 26, illuminated spots 52 at other locations may beout-of-focus. Therefore, the light intensity of the returned light beamsof the focused spots will be at its peak, while the light intensity atother spots will be off peak. Thus, for each illuminated spot, lightintensity is measured for different relative spatial dispositionsbetween the endoscope 46 and the teeth 26. Typically, the derivative ofthe intensity over time will be made, and the relative spatialdisposition(s) between the endoscope 46 and the teeth 26 wherein thederivative equals zero can be used to generate data that is used inconjunction with the relative spatial dispositions between the endoscope26 and the teeth 26 to determine surface topography of the teeth. Aspointed out above, as a result of use of the mirror with aperture 40,the incident light forms a light disk on the surface when out of focusand a sharply-focused light spot only when in focus. Consequently, thedistance derivative will exhibit a larger change in magnitude whenapproaching an in-focus position, thus increasing accuracy of themeasurement.

The light reflected from each of the illuminated spots 52 includes abeam travelling initially in the Z-axis in the opposite direction of theoptical path traveled by the incident light beams. Each returned lightbeam 54 corresponds to one of the incident light beams 36. Given theasymmetrical properties of mirror 40, the returned light beams 54 arereflected in the direction of a detection assembly 60. The detectionassembly 60 includes a polarizer 62 that has a plane of preferredpolarization oriented normal to the polarization plane of polarizer 32.The returned polarized light beam 54 pass through imaging optics 64,typically a lens or a plurality of lenses, and then through an array ofpinholes 66. Each returned light beam 54 passes at least partiallythrough a respective pinhole of the array of pinholes 66. A sensor array68, which can be a charge-coupled device (CCD) or any other suitableimage sensor, includes a matrix of sensing elements. In manyembodiments, each sensing element represents a pixel of the image andeach sensing element corresponds to one pinhole in the array 66.

The sensor array 68 is connected to an image-capturing module 80 of theprocessor unit 24. The light intensity measured by each of the sensingelements of the sensor array 68 is analyzed, in a manner describedbelow, by the processor 24. Although the optical device 22 is depictedin FIGS. 1A and 1B as measuring light intensity, the device 22 can alsobe configured to measure other suitable characteristics (e.g.,wavelength, polarization, phase shift, interference, dispersion), aspreviously described herein. In many embodiments, the plane of thesensor array 68 is orthogonal to the returned light beams 54 (e.g.,orthogonal to a direction of propagation of the returned light beams).In some embodiments, the plane of the sensor array 68 is non-orthogonalto the returned light beams 54, as described below.

The optical device 22 includes a control module 70 that controlsoperation of the semi-conducting laser 28. The control module 70synchronizes the operation of the image-capturing module 80 with theoperation of the laser 28 during acquisition of data representative ofthe light intensity (or other characteristic) from each of the sensingelements. The intensity data and data of relative spatial dispositionsbetween the endoscope 46 and the teeth 26 are processed by the processor24 per processing software 82 to obtain data representative of thethree-dimensional topography of the external surfaces of the teeth 26.Exemplary embodiments of methods for processing the data of thecharacteristic and relative spatial disposition data are describedbelow. A resulting three-dimensional representation of the measuredstructure can be displayed on a display 84 and manipulated for viewing(e.g., viewing from different angles, zooming-in or out) by a usercontrol module 85 (typically a computer keyboard). In addition, the datarepresentative of the surface topography can be transmitted through anappropriate data port such as, for example, a modem 88 or any suitablecommunication network (e.g., a telephone network, the internet) to arecipient (e.g., to an off-site CAD/CAM apparatus).

By capturing relative distance data between the endoscope 46 and thestructure being measured for different relative spatial dispositionsbetween the endoscope 46 and the structure (e.g., in the case of a teethsegment, from the buccal direction, lingual direction and/or optionallyfrom above the teeth), an accurate three-dimensional representation ofthe structure can be generated. The three-dimensional data and/or theresulting three-dimensional representation can be used to create avirtual model of the three-dimensional structure in a computerizedenvironment and/or a physical model fabricated in any suitable fashion(e.g., via a computer controlled milling machine, a rapid prototypingapparatus such as a stereolithography apparatus or 3D printingapparatus).

Referring now to FIGS. 2A and 2B, a probing member 90 is illustrated inaccordance with many embodiments. In many embodiments, the probingmember 90 forms at least a portion of the endoscope 46. The probingmember 90 can be made of a light transmissive material (e.g., glass,crystal, plastic, etc.) and includes a distal segment 91 and a proximalsegment 92, tightly glued together in an optically transmissive mannerat 93. A slanted face 94 is covered by a reflective mirror layer 95. Atransparent disk 96 (e.g., made of glass, crystal, plastic, or any othersuitable transparent material) defining a sensing surface 97 is disposedalong the optical path distal to the mirror layer 95 so as to leave anair gap 98 between the transparent disk 96 and the distal segment 91.The transparent disk 96 is fixed in position by a holding structure (notshown). Three light rays 99 are represented schematically. As can beseen, the light rays 99 reflect from the walls of the probing member 90at an angle in which the walls are totally reflective, reflect from themirror layer 95, and then propagate through the sensing face 97. Whilethe light rays 99 can be focused external to the probing member 90 withany suitable combination of respective focal lengths, in manyembodiments, the light rays 99 are focused on a focusing plane 100external to the probing member 90. For example, as illustrated in FIG.2C, which shows an end view III-III of the probing member 90, the lightrays 99 are focused to a common focal length, thereby being focused on afocusing plane 100 that is perpendicular to the direction of propagationof the light rays 99 external to the probing member 90 (also referred toherein as the Z-axis). As another example, as illustrated in FIG. 2D,which shows an end view III-III of the probing member 90, the light rays99 are focused to different focal lengths so as to be focused on afocusing plane 100 that is non-perpendicular to the Z-axis. While twoconfigurations of focal positions are illustrated and described, anysuitable configuration of focal positions can be employed.

FIGS. 3A and 3B illustrate an optical probe 200 scanning a structure 202in a global Cartesian reference frame 204, in accordance with manyembodiments. (FIG. 3B shows the cross-sectional view I-I as defined inFIG. 3A). The optical probe 200 can be used with any suitable scanningdevice or system described herein, such as the optical device 22. Atwo-dimensional array of incident light beams 206 emanating from theoptical probe 200 are arranged in a plurality of rows extending in the Xdirection, including a first row 208 and a last row 210. Each row of thearray of light beams 206 is focused to a respective common focal lengthalong the Z direction, thereby forming a diagonal focal plane 212. Thefocal lengths of the first row 208 and the last row 210 differ by apredetermined length 214 in the Z direction. The optical probe 200 canbe moved relative to the structure 202 to scan the structure 202 withthe light beams 206. For example, as depicted in FIG. 3B, the opticalprobe 200 can be translated in the Y direction from a first position 216to a second position 218.

In many embodiments, each row in the array of light beams 206 is focusedto a different depth along the Z direction so as to produce a focalplane 212 that is not orthogonal to the Z-axis. Therefore, as theoptical probe 200 is moved relative to the structure 202, the focalplane 212 of the light beams 206 sweeps through a three-dimensionalvolume of the structure 202. For example, as the optical probe 200translates from position 216 to position 218, the focal plane 212 sweepsa three-dimensional volume having a Z depth 214. Accordingly, theoptical probe 200 can scan the structure 202 in the Z direction throughcontinuous movement of the optical probe 200 relative to structure 202,while maintaining constant respective focal lengths of the light beams206. Although FIG. 3B depicts movement of the optical probe 200 in the Ydirection, in many embodiments, the optical probe 200 can be moved withsix degrees of freedom (e.g., three degrees of freedom in translationand three degrees of freedom in rotation) to a plurality of differentrelative positions and/or orientations between the optical probe 200 andthe structure 202.

The array of light beams 206 can be provided in any suitableconfiguration. For example, the array of light beams 206 can be focusedto any suitable number of different focal lengths relative to theoptical probe 200, such as 3, 5, 10, 50, or 100 or more different focallengths. The focal lengths of the array of light beams 206 can beconfigured to have any suitable range, such as at least 5 mm, 7.5 mm, or10 mm or more. The focal lengths of the first row 208 and the last row210 in the array of light beams 206 can be different by any suitablelength, such as by 5 mm or less, 10 mm, 15 mm, or 25 mm or greater. Forexample, the focal lengths can be different by a length within the rangeof 5 mm to 25 mm.

The array of light beams 206 can be generated by any system or devicesuitable for focusing a wavelength component of each of the light beamsto a respective focal position (e.g., a diagonal focal plane 212). Inmany embodiments, one or more optics of the optical device 22 can beused to focus an array of light beams to a plurality of fixed focalpositions relative to the probe. For example, suitable embodiments ofthe optics described herein can be included within the grating or microlens array 38, focusing optics 42, relay optics 44, optics within theendoscope 46, or suitable combinations thereof. The optics can beconfigured to be used with telecentric and/or non-telecentric confocalfocusing optics.

FIG. 4A illustrates an optical assembly 300 for focusing a plurality oflight beams to respective focal positions, in accordance with manyembodiments. In the optical assembly 300, an array of light beams 302emanate from a source array 304 (e.g., a micro lens array), are focusedby focusing optics 306, and reflect off a mirror 308 (e.g., a mirrordisposed within an endoscopic probing member) to form a focal plane 310.The mirror 308 can be positioned at a 45° angle relative to the opticalaxis in order to produce an orthogonal focal plane 310.

FIG. 4B illustrates an optical assembly 320 for focusing a plurality oflight beams to a diagonal focal plane, in accordance with manyembodiments. Similar to the optical assembly 300, the system 320includes a source array 324 that produces an array of light beams 322,focusing optics 326, and a mirror 328. The mirror 328 is tilted at asuitable angle relative to the optical axis, such as a 30° angle, inorder to produce a focal plane 330 that is inclined relative to thescanner 332. The focal plane 330 can be used to scan a three-dimensionalstructure, such as a tooth 334, using fixed focal positions as describedherein.

FIG. 5 illustrates a micro lens array 400 for focusing an array of lightbeams to a diagonal focal plane, in accordance with many embodiments.The micro lenses (e.g., micro lens elements 402) of micro lens array 400are arranged in a plurality of rows 404, including a first row 406 and alast row 408. Each row of micro lenses is configured to focus lightbeams to a different focal length, thereby producing a diagonal focalplane.

FIG. 6A illustrates an optical assembly 500 for focusing a plurality oflight beams to a diagonal focal plane, in accordance with manyembodiments. The optical assembly 500 includes a tilted source array502, which can be a micro lens array tilted at a suitable angle relativeto the optical axis. The array of light beams 504 produced by the tiltedsource array 502 passes through focusing optics 506, and reflects offmirror 508 to form a diagonal focal plane 510, suitable for scanning thestructure 512 with fixed focal positions as described herein. FIG. 6Billustrates the optical path of returned light beams 514 through theoptical assembly 500. The returned light beams 514 reflected from thestructure 512 pass back through the focusing optics 506, and aredirected by beam splitter 516 onto the sensor array 518. As previouslydescribed, the sensor array 518 can include a plurality of sensorelements arranged in a plane. In many embodiments, the sensor array 518is non-orthogonal relative to the returned light beams 514, such thatthe plane of sensor elements is tilted relative to the direction ofpropagation of the returned light beams 514. The plane can be tilted bythe same amount as the source array 502 in order to allow for confocalsensing of the returned light beams 502.

FIG. 7A illustrates an optical assembly 600 for focusing a plurality oflight beams to a diagonal focal plane, in accordance with manyembodiments. FIG. 7B illustrates an unfolded configuration of theoptical assembly 600. In the optical assembly 600, an array of lightbeams 604 emanating from a source array 602 pass through focusing optics606. A non-symmetric optics 608 is disposed between the focusing optics606 and a mirror 610 and configured to focus the light beams to adiagonal focal plane 612 suitable for scanning the structure 614 withfixed focal positions as described herein. Any suitable optical elementor combination of optical elements can be used for the non-symmetricoptics 608. For example, the non-symmetric optics 608 can include anoff-axis lens tilted at a suitable angle relative to the optical axis.Alternatively or in combination, the non-symmetric optics 608 caninclude a Fresnel lens including a plurality of segments configured torefract each of the plurality of light beams to a respective focalposition in order to produce a suitable diagonal focal plane.

The global surface topography of the structure can be reconstructed byspatially aligning the local intensity data to each other. In manyembodiments, the relative position and/or orientation between theoptical probe and the structure during the scanning procedure is used todetermine the spatial relationships between the intensity data andthereby align the data. Any suitable method or combination of methodscan be used to track the position and/or orientation of the opticalprobe or a suitable portion of the optical probe (e.g., the scanning tipof the endoscope 46 or probing member 90) relative to the structure,such as a suitable motion estimation or motion tracking method. Forexample, one or more motion tracking devices can be used to generatemotion data suitable for determining the position and/or orientation ofthe optical probe relative to the three-dimensional structure.

In many embodiments, an optical tracking method is used to determine thespatial disposition of the probe relative to the structure with respectto six degrees of freedom. For example, the motion tracking device caninclude an external camera (or any other suitable image sensor) togenerate image data of the probe as it is moved between a plurality ofdifferent positions and/or orientations during the scanning procedure.The camera can capture images of any suitable portion of the probe, suchas a portion positioned outside of the patient's intraoral cavity.Alternatively or in combination, the camera can capture images of one ormore suitable markers (e.g., included in motion tracking element 47)placed on one or more suitable portions of the probe. The images can beprocessed to estimate the position and/or orientation of the proberelative to the structure using any suitable machine vision method(e.g., a structure from motion algorithm, a photogrammetric method, animage registration/alignment method, and/or an optical flow estimationmethod such as a Lucas-Kanade method). Optionally, a camera can beintegrated into or coupled with the probe, such that image data capturedby the camera can be analyzed using a suitable ego-motion estimationmethod, such as the machine vision methods described herein, todetermine the position and/or orientation of the probe relative to thestructure.

Alternatively or in combination, the motion tracking device can utilizeinertial-based estimation methods to determine the relative positionand/or orientation of the probe. For example, the motion sensor caninclude an inertial measurement unit, such as an inertial sensor. Theinertial sensor can be a micro electromechanical system (MEMS) device.In many embodiments, the inertial sensor includes a plurality ofaccelerometers and/or a plurality of gyroscopes configured to detectmotion of the probe with respect to three degrees of translation and/orthree degrees of rotation.

In another example, an electromagnetic tracking (EMT) system can be usedto track the position and/or orientation of the probe relative to thestructure. For instance, an EMT field can be provided by a suitablegenerator or transmitter, and the position and/or orientation of an EMTsensor within the field (e.g., with respect to up to three degrees offreedom in rotation and three degrees of freedom in translation) can bedetermined based on the electromagnetic signals detected by the sensor.Any suitable number and configuration of EMT field generators and EMTsensors can be used. For example, an EMT field generator can be situatedat a fixed location at the site of the scanning procedure (e.g., coupledto an operating table or patient chair) and an EMT sensor can bedisposed on the probe (e.g., included in motion tracking element 47) totrack the motion of the probe. In many embodiments, EMT sensors are alsobe placed on or near the three-dimensional structure (e.g., on apatient's head, face, jaw, and/or teeth) in order to account for anymotion of the structure during the measurement procedure. Alternativelyor in combination, the EMT field generator can be placed on thestructure and used to track the relative motion of a probe having acoupled EMT sensor. Conversely, the EMT field generator can be locatedon the probe and the EMT sensor can be located on the structure.

Any suitable method can be used to process the motion data to determinethe position and/or orientation of the probe relative to the structure.For example, the data can be processed using a motion tracking algorithmcombined with a Kalman filter. Optionally, the processing can utilizemotion data received from a plurality of the different types of motiontracking systems and devices described herein.

FIG. 8 is a simplified block diagram depicting acts of a method 700 formeasuring surface topography of a three-dimensional structure, inaccordance with many embodiments. Any suitable optical devices orsystems, such as the embodiments described herein, can be used topractice the method 700.

In act 710, a plurality of incident light beams is generated. In manyembodiments, the optical device 22 can be used to form a two-dimensionalpattern of light beams as described herein.

In act 720, each of the plurality of incident light beams is focused toa respective focal position relative to an optical probe. Any suitablefocusing mechanism can be used, such as the embodiments describedherein. In many embodiments, the light beams are focused to form adiagonal focal plane to provide Z scanning with motion of the probe, aspreviously described herein.

In act 730, a three-dimensional structure is illuminated with theincident light beams for a plurality of relative positions and/ororientations between the probe and the structure. In many embodiments,the light beams are focused to a diagonal focal plane such that movementof the probe through a plurality of positions and/or orientationsrelative to the structure enables three-dimensional scanning of thestructure, as described herein. A plurality of returning light beams areproduced by illuminating the structure with the incident light beams,with each returning light beam corresponding to an incident light beam.

In act 740, a characteristic of each of a plurality of light beamsreturning from the three-dimensional structure is measured. Aspreviously mentioned, the characteristic can be any suitable measurableparameter of the light beams, such as intensity, wavelength,polarization, phase shift, interference, or dispersion. Any suitabledevice configured to measure the characteristic of each of the lightbeams can be used. For example, a suitable detector unit, such as asensor (e.g., sensory array 68) including a two-dimensional array ofsensor elements can be used, as previously described herein. The sensorarray can be orthogonal or non-orthogonal to the returning light beams,based on the configuration of the focusing optics and the light sourcearray.

In act 750, the measured characteristic and the corresponding relativepositions and/or orientations between the optical probe and thestructure are processed (e.g., by processor 24) to generate surfacetopography data for the structure. Any suitable method for processingthe data of the measured characteristic can be used, such as theembodiments described herein. In many embodiments, the data of themeasured characteristic is aligned based on data obtained by trackingthe relative position and/or orientation of the optical probe (e.g.,motion data and/or image data) as described herein.

In act 760, surface topography for the three-dimensional structure isgenerated, such as by the processor 24 as described herein. Theresultant three-dimensional representation of the structure can be usedfor any suitable application, such as the dental and orthodonticprocedures described herein.

While preferred embodiments of the present invention have been shown anddescribed herein, it will be obvious to those skilled in the art thatsuch embodiments are provided by way of example only. Numerousvariations, changes, and substitutions will now occur to those skilledin the art without departing from the invention. It should be understoodthat various alternatives to the embodiments of the invention describedherein may be employed in practicing the invention. It is intended thatthe following claims define the scope of the invention and that methodsand structures within the scope of these claims and their equivalents becovered thereby.

What is claimed is:
 1. An apparatus for measuring surface topography ofa three-dimensional structure, the apparatus comprising: an opticalprobe moveable relative to the three-dimensional structure; anillumination unit configured to generate a plurality of incident lightbeams, each of the plurality of incident light beams comprising a firstwavelength component; an optical system configured to focus the firstwavelength component of each of the plurality of incident light beams toa respective fixed focal position relative to the optical probe whilemeasuring the surface topography; and a detector unit configured tomeasure a characteristic of each of a plurality of returned light beamsthat are generated by illuminating the three-dimensional structure withthe plurality of incident light beams.
 2. The apparatus of claim 1,wherein the characteristic is intensity.
 3. The apparatus of claim 1,wherein the detector unit comprises a two-dimensional array of sensorelements, each sensor element of the two-dimensional array of sensorelements being configured to measure the characteristic from acorresponding returned light beam of the plurality of returned lightbeams.
 4. The apparatus of claim 3, wherein the optical system isconfigured to form a two-dimensional pattern of the plurality ofincident light beams from light generated by the illumination unit, thetwo-dimensional pattern of the plurality of incident light beamscorresponding to the plurality of returned light beams measured by thetwo-dimensional array of sensor elements.
 5. The apparatus of claim 4,wherein the optical system comprises an optics expander unit configuredto expand light generated by the illumination unit to form thetwo-dimensional pattern of the plurality of incident light beams.
 6. Theapparatus of claim 3, wherein the illumination unit is configured toproduce a two-dimensional pattern of the plurality of incident lightbeams corresponding to the plurality of returned light beams measured bythe two-dimensional array of sensor elements.
 7. The apparatus of claim3, wherein: the plurality of incident light beams are arranged in aplurality of rows having a first row and a last row; incident lightbeams in each row are focused to a respective common focal length; andthe respective common focal lengths of the first row and the last roware different by a predetermined length.
 8. The apparatus of claim 7,wherein the predetermined length is from 5 mm to 25 mm.
 9. The apparatusof claim 3, wherein the two-dimensional array of sensor elements isarranged in a plane that is oriented for confocal sensing of theplurality of returned light beams relative to focal lengths of the firstwavelength component of the plurality of incident light beams.
 10. Theapparatus of claim 9, wherein the plane of the two-dimensional array ofsensor elements is non-orthogonal to the plurality of returned lightbeams.
 11. The apparatus of claim 1, wherein the optical system isconfigured to focus the first wavelength component of the plurality ofincident light beams to at least 10 different focal lengths relative tothe scanner, and wherein the at least 10 different focal lengths have arange of at least 10 mm.
 12. A method of measuring surface topography ofa three-dimensional structure, the method comprising: focusing a firstwavelength component of each of a plurality of incident light beams to arespective fixed focal position relative to an optical probe whilemeasuring the surface topography; and measuring a characteristic of eachof a plurality of returned light beams that are generated byilluminating the three-dimensional structure with the plurality ofincident light beams for one or more of a plurality of differentrelative positions or a plurality of different orientations between theoptical probe and the three-dimensional structure.
 13. The method ofclaim 12, wherein the characteristic is intensity.
 14. The method ofclaim 12, comprising tracking changes in one or more of relativeposition or orientation between the optical probe and thethree-dimensional structure.
 15. The method of claim 14, wherein: theplurality of incident light beams are arranged in a plurality of rowshaving a first row and a last row; incident light beams in each row arefocused to a respective common focal length; and the respective commonfocal lengths of the first row and the last row are different by apredetermined length.
 16. The method of claim 15, wherein thepredetermined length is at least 10 mm.
 17. The method of claim 14,wherein the first wavelength component of the plurality of incidentlight beams is focused to at least 10 different focal lengths relativeto the scanner, and wherein the at least 10 different focal lengths havea range of at least 10 mm.
 18. The method of claim 12, furthercomprising generating the plurality of incident light beams.
 19. Themethod of claim 18, wherein the measuring step is performed using atwo-dimensional array of sensor elements, each sensor element of thetwo-dimensional array of sensor elements being configured to measure thecharacteristic from a corresponding returned light beam of the pluralityof returned light beams.
 20. The method of claim 19, wherein theplurality of incident light beams are generated as a two-dimensionalpattern, and the two-dimensional pattern of the plurality of incidentlight beams corresponds to the plurality of returned light beamsmeasured by the two-dimensional array of sensor elements.